Abstract

We investigate the generalized Hyers-Ulam-Rassias stability problem in quasi-β-normed spaces and then the stability by using a subadditive function for the generalized quartic function f:X→Y such that f(ax+by)+f(ax−by)−2a2(a2−b2)f(x)=(ab)2[f(x+y)+f(x−y)]−2b2(a2−b2)f(y), where a≠0, b≠0, a±b≠0, for all x,y∈X.